Question

If a, b, c, d and e are five natural numbers, then find the number of ordered sets(a, b, c, d, e) possible such that a+b+c+d+e=75.

(a) ^65C5

(b) ^58C6

(c) ^72C7

(d) ^74C4

The question was posed to me in final exam.

My enquiry is from Counting topic in chapter Counting of Discrete Mathematics

Answer 1

Correct option is (d) ^74C4

For explanation: Let assumes that there are 75 identical balls which are to be arranged in 5 different compartments (Since a, b, c, d, e are distinguishable). If the balls are arranged in the row. We have 74 gaps where we can place a ball in each gap since we need 5 compartments we need to place only 4 balls. We can do this in ^74C4 ways.